I've a math problem that I like to solve.

Let $\displaystyle L$ be a line and let $\displaystyle p$ be a point. Show that the orthogonal projection

of $\displaystyle p$ onto $\displaystyle L$ is the unique point $\displaystyle w$ on $\displaystyle L$ for which the distance from $\displaystyle p$

to $\displaystyle w$ is minimized.

Is it possible to tell me how I can prove this using differential geometry?